It is said that the best ice cream in Paris is from Berthillon. Fortunately, they have their own store right in the center of Ile St Louis. Unfortunately, it is very popular.
The long line is for the take away vending counter. You can get some scoops in a cone or dish and then eat as you continue your sight seeings.
To the left of the entrance for the take away counter is the entrance for a “tea room.” There might be a wait there, but it does not get a huge line as the line would not move quickly at all. This is sit down for some confection with tea or coffee.
Many other places on Ile St Louis also sell Berthillon ice cream to take away, but their official store seems to attract the biggest crowds.